Optimal convergence properties of the FETI domain decomposition method

Farhat, Charbel; Mandel, Jan; Roux, F. X.

doi:10.1016/0045-7825(94)90068-x

Cited by 321 publications

(233 citation statements)

References 15 publications

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“…An important advance, which made the rate of convergence of the iteration less sensitive to the number of unknowns of the local problems, was made by Farhat, Mandel, and Roux a few years later [14]. Our own work is based on the pioneering work by Mandel and Tezaur [24], who fully analyzed a variant of that algorithm.…”

Section: Introductionmentioning

confidence: 99%

FETI and Neumann-Neumann iterative substructuring methods: Connections and new results

Klawonn

Widlund

2000

Comm. Pure Appl. Math.

165

179

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Section: Introductionmentioning

confidence: 99%

FETI and Neumann-Neumann iterative substructuring methods: Connections and new results

Klawonn

Widlund

2000

Comm. Pure Appl. Math.

165

179

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“…PermonFLLOP (FETI Light Layer on Top of PETSc) is an extension of the PermonQP package, implementing the algebraic part of DDMs of the FETI type [7], [6], [5], [4]. Let us show how PermonFLLOP is implemented from the user's perspective.…”

Section: Permonfllopmentioning

confidence: 99%

“…We strive to maximize the number of subdomains to reduce the sizes of the subdomain stiffness matrices, accelerating their factorization and K † actions. Furthermore, thanks to the FETI operator condition number estimate [6], decomposition into more subdomains maintaining a fixed discretization parameter h leads to reduction of the condition number of K and thus the number of iterations.…”

Section: Coarse Problemmentioning

confidence: 99%

Parallel strategies for solving the FETI coarse problem in the PERMON toolbox

Vašatová¹,

Tomčala²,

Sojka³

et al. 2017

Programs and Algorithms of Numerical Mathematics 18

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“…Dostál et al [2]. The newly formulated problem exhibits both numerical and parallel scalabilities [4], which is essential for effective application to high performance computers.…”

Section: Outline Of Theorymentioning

confidence: 99%

“…Dostál et al [2]. The newly formulated problem exhibits both numerical and parallel scalabilities [4], which is essential for effective application to high performance computers.If concept of the FETI method is applied to solution to the contact problems, basically the same methodology can be used to prescribe conditions of nonpenetration between bodies in contact [2]. …”

mentioning

confidence: 99%

Total FETI for contact problems with additional nonlinearities

Dobiáš

Pták

Vondrák

et al. 2008

Proc Appl Math and Mech

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The paper is concerned with application of a new variant of the Finite Element Tearing and Interconnecting (FETI) method, referred to as the Total FETI (TFETI), to the solution to contact problems with additional nonlinearities. While the standard FETI methods assume that the prescribed Dirichlet conditions are inherited by subdomains, TFETI enforces both the compatibility between subdomains and the prescribed displacements by the Lagrange multipliers. If applied to the contact problems, this approach not only transforms the general nonpenetration constraints to the bound constraints, but it also generates an enriched natural coarse grid defined by the a priori known kernels of the stiffness matrices of the subdomains exhibiting rigid body modes. We combine our in a sense optimal algorithms for the solution to bound and equality constrained problems with geometric and material nonlinearities. The section on numerical experiments presents results of solution to bolt and nut contact problem with additional geometric and material nonlinear effects. Outline of theoryThe FETI class of nonoverlapping spatial domain decompositions was introduced by Farhat and Roux in their landmark paper [1]. The basic idea of the FETI methods is that the compatibility between subdomains, into which the original domain is partitioned, is enforced by the Lagrangian multipliers with physical meaning of forces in this mechanical context. Within the framework of the FETI concept, these forces are called the dual variables unlike the displacements which are referred to as the primal variables.After eliminating the primal variables, the original problem is reduced to a small, relatively well conditioned, typically equality constrained quadratic programming problem that is solved iteratively, see e.g. Dostál et al. [2]. The newly formulated problem exhibits both numerical and parallel scalabilities [4], which is essential for effective application to high performance computers.If concept of the FETI method is applied to solution to the contact problems, basically the same methodology can be used to prescribe conditions of nonpenetration between bodies in contact [2]. Total FETIConsider a steady-state contact problem of solid deformable bodies, which constitutes a 2nd order elliptic boundary value problem. The mathematical formulation of the problem is given by the governing equations expressing equilibrium conditions of the system, along with the boundary conditions, see e.g. [3, Chapter 2].The process of partitioning original domain into subdomains in general generates some subdomains, which are well constrained, others which are only partly constrained, and the remaining, which are totally unconstrained. All the subdomains which are not well constrained can move like rigid bodies, or they exhibit rigid body modes, so that their stiffness matrices are singular with dimensions of their kernels, or their defects, ranging from 1 to 6 for 3D problems.The original FETI method assumes that the Dirichlet boundary conditions are inherited from the ...

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Optimal convergence properties of the FETI domain decomposition method

Cited by 321 publications

References 15 publications

FETI and Neumann-Neumann iterative substructuring methods: Connections and new results

FETI and Neumann-Neumann iterative substructuring methods: Connections and new results

Parallel strategies for solving the FETI coarse problem in the PERMON toolbox

Total FETI for contact problems with additional nonlinearities

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